The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008
In Equation 11, the weight matrix W is equal to W = ct^V,” 1
where \ ( includes the a’ posteriori partial covariance matrices
of each best estimation, of each solution.
It should be mentioned that due to the fact that partial solutions
are non-correlated, the best estimation of Equation 11 is
equivalent to the corresponding estimation. This can be
calculated from the simultaneous solution of buildings and
LiDAR points, which have taken place in the initial solutions of
the system 10 through Equations 6 and 7. The a’ posteriori
standard deviation of unit weight a 2 0 with the corresponding
covariance matrices of the parameters and the observations are
calculated based on Equations 8, 9 and 13.
(12)
contain 4 LiDAR strips (point cloud) and a block of 4 aerial
images strips over the same area, each containing 4 images
(Figure 2). For both sensors, an integrated GPS/IMU system
provided the georeferencing. Traditional aerotriangulation was
performed on aerial images using GCPs measured by geodetic
means (0.1m stdv) producing the EO (Exterior Orientation).
The bundle adjustment resulted in positioning accuracies (EO
parameters) averaging 0.08, 0.08, and 0.10 meters in X, Y, and
Z, respectively. The orientation accuracies average 10, 10, and
9 arcsecs in co, cp, k, respectively.
In the central part of the survey (also called “test field”) 24
buildings, mainly medium sized, have been selected and
photogrammetrically restituted (point dataset). These buildings
(called ‘buildings-positions’) are located in the overlapping area.
In Figure 2, an image mosaic, the selected buildings and
LiDAR strips are illustrated. These buildings are assumed as the
reference dataset. The area which is occupied by the selected
group of buildings is about 300,000 m 2 with a perimeter of
2250 m.
=OoA(a t Wa)~ 1 A T (13)
The statistical valuation of the adjustment’s results concerns not
only the assumptions, which have been made (initial hypothesis
H 0 ) related to mathematical and statistical model of adjustment,
but also the reliability of the observations.
As it has been mentioned, that proposed method assumes that
the reference dataset is derived by photogrammetric means
(surface P) and the target dataset consists of the corresponding
LiDAR points (surface Q) captured over the same overlapped
area. It should be mentioned that the reference dataset can be
derived by any other source such as by terrestrial laserscanning.
But in this research, they were aerial photos of interest.
The general check of this hypothesis H 0 is achieved by using
the ratio K/ a l in combination with the % 2 distribution, with r
degree of freedom.
The hypothesis H 0 , according to the reliability of the
observations, is checked based on the ratio v iy /o.. of each
observation i by using the normal distribution z for a level
meaningfulness a=0.001.
The data snooping procedure led to the conclusion that
approximately 4%-5% of the observations include outliers. The
above results are in agreement with what have been proven in
Pothou et al., 2007.
4. DATA DESCRIPTION
After implementing the proposed method, it was first tested on
the simulated data for boresight misalignment estimation
(Pothou et al., 2007). Next a new dataset, provided by ODOT
(Ohio Department of Transportation) and CFM (The Center for
Mapping, OSU) was used for intensive testing. In London,
Madison County, Ohio, LiDAR point clouds and direct digital
aerial images were collected in several missions over an urban
test area. The city includes mainly residential houses and a few
bigger buildings (such as warehouses and factories).
The 55 mm focal length, DSS digital camera, with 9pm pixel
size, was laboratory calibrated prior to the test flights. The test
area was simultaneously surveyed by an Optech ALTM 30/70
LiDAR system of the Ohio Department of Transportation. At
FOV of 40°, 50 Hz scanner frequency and 70 kHz pulse rate,
the point density was about 5-8 points/m 2 . A set of 16 images
with adequate coverage of the region, which contained survey
control points, was identified. The flight plan consisted of two
parallel strips and two perpendicular strips. Therefore, the data
Figure 2: Highlighted buildings distributed in the area and
LiDAR strips’ orientation
5. EXPERIMENTS AND RESULTS
The first part of the algorithm is an enhanced version of Pothou
et al., 2007 method which calculates the boresight
misalignment parameters and their standard deviation for each
strip over each individual building. In this individual solution a
data snooping procedure eliminates outliers before estimating
the boresight parameters (Equation 7). The second part of the
algorithm calculates the total solution (Equation 11) where
combinations of buildings and strips are involved (with their
individual weights).